Spring 2004

Instructor: T. Y. Lam

Time: MWF 11 a.m.

Room: 71 Evans

**Syllabus: **

Sets, mappings, relations and equivalence relations. Arithmetic of the integers (including prime factorizations, euclidean algorithms, greatest common divisors and least common multiples).

The concept of groups and subgroups. Additive and multiplicative groups. Cyclic groups, permutation groups and matrix groups. Orders of elements, and coset decompositions. The notions of normal subgroups and quotient groups. Basic homomorphism theorems.

Elements of ring theory (mostly for commutative rings). Number rings and polynomial rings. The notions of ideals and quotient rings.

Elements of field theory: field extensions and field extension degrees. Transitivity formula. Some constructions of finite fields.

**Grades:** Letter grades only, based on:
20% Homework, 30% Midterm, 50% Final.